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Simplifying 0 = 0.4080t2 + -1.394t + 1.589 Reorder the terms: 0 = 1.589 + -1.394t + 0.4080t2 Solving 0 = 1.589 + -1.394t + 0.4080t2 Solving for variable 't'. Combine like terms: 0 + -1.589 = -1.589 -1.589 + 1.394t + -0.4080t2 = 1.589 + -1.394t + 0.4080t2 + -1.589 + 1.394t + -0.4080t2 Reorder the terms: -1.589 + 1.394t + -0.4080t2 = 1.589 + -1.589 + -1.394t + 1.394t + 0.4080t2 + -0.4080t2 Combine like terms: 1.589 + -1.589 = 0.000 -1.589 + 1.394t + -0.4080t2 = 0.000 + -1.394t + 1.394t + 0.4080t2 + -0.4080t2 -1.589 + 1.394t + -0.4080t2 = -1.394t + 1.394t + 0.4080t2 + -0.4080t2 Combine like terms: -1.394t + 1.394t = 0.000 -1.589 + 1.394t + -0.4080t2 = 0.000 + 0.4080t2 + -0.4080t2 -1.589 + 1.394t + -0.4080t2 = 0.4080t2 + -0.4080t2 Combine like terms: 0.4080t2 + -0.4080t2 = 0.0000 -1.589 + 1.394t + -0.4080t2 = 0.0000 Begin completing the square. Divide all terms by -0.4080 the coefficient of the squared term: Divide each side by '-0.4080'. 3.894607843 + -3.416666667t + t2 = 0 Move the constant term to the right: Add '-3.894607843' to each side of the equation. 3.894607843 + -3.416666667t + -3.894607843 + t2 = 0 + -3.894607843 Reorder the terms: 3.894607843 + -3.894607843 + -3.416666667t + t2 = 0 + -3.894607843 Combine like terms: 3.894607843 + -3.894607843 = 0.000000000 0.000000000 + -3.416666667t + t2 = 0 + -3.894607843 -3.416666667t + t2 = 0 + -3.894607843 Combine like terms: 0 + -3.894607843 = -3.894607843 -3.416666667t + t2 = -3.894607843 The t term is -3.416666667t. Take half its coefficient (-1.708333334). Square it (2.918402780) and add it to both sides. Add '2.918402780' to each side of the equation. -3.416666667t + 2.918402780 + t2 = -3.894607843 + 2.918402780 Reorder the terms: 2.918402780 + -3.416666667t + t2 = -3.894607843 + 2.918402780 Combine like terms: -3.894607843 + 2.918402780 = -0.976205063 2.918402780 + -3.416666667t + t2 = -0.976205063 Factor a perfect square on the left side: (t + -1.708333334)(t + -1.708333334) = -0.976205063 Can't calculate square root of the right side. The solution to this equation could not be determined.
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